Examples for 9th grade

Enterprise and wages The enterprise operates a total 162 workers and their average salary is M dollars. If the company has hire an additional 18 employees whose average wage would be the S dollars, would reduce the overall average salary in the company of 3.6%. Calculate th

Tourists From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 47 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group?

Painters The first team of painters would paint bridge in 15 days, the second in 10 days. After 3 days of working together second team goes out and continue only first team. How many days took second team to finish painting the bridge?

Sinus Determine the smallest integer p for which the equation 4 sin x = p has no solution.

Trousers Jarek bought new trousers, but the trousers were too long. Their length was in the ratio 5: 8 to Jarek height. Mother his trousers cut by 4 cm, thus the original ratio decreased by 4%. Determine Jarek's high.

Unknown number Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The prod

Hockey players After we cycle five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other?

Two diggers There are two diggers. One digger digs a pit 46 hours second gidding 2 times faster. a) how long took to dig a pit second digger b) how long took dig together

Nuts, girl and boys Milena collected fallen nuts and called a bunch of boys let them share. She took a condition: the first boy takes one nut and tenth of the rest, the second takes 2 nuts and tenth new rest, the third takes 3 nuts and tenth new rest and so on. Thus managed

Quadratic function It is given a quadratic function y = -4x2+5x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.

Triangular prism Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.

Target Peter, Martin and Jirka were fire in a special target, which had only three fields with values of 12, 18 and 30 points. All boys were firing with the same number of arrows and all the arrows hit the target, and the results of every two boys differed in on

Line Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.

Logistics Head of logistics department informed the meeting of management of the same item is currently not available in sufficient quantity in all three warehouses of the company. We have the total 135 pieces. It was 37 pieces more in the warehouse No. 3 than in t

The dice What is the probability of events that if we throw a dice is rolled less than 6?

Hexagon 5 The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon.

Mother and daughter 2 The mother is 40 years older than her daughter. How old is the mother if her age is eight thirds age of daughter?

Medal Calculate the approximate weight of the gold Olympics medal, if its diameter is 8 cm and a thickness 6 mm. The density of gold find out in the tables or on the Internet.

Mystery of stereometrie Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.